On the Energy Efficient Displacement of Random Sensors for Interference and Connectivity (1611.06329v3)

Abstract: This paper investigates the problem of the minimilization of energy consumption in reallocation of wireless mobile sensors network (WMSN) to assure good communication without interference. Fix $d\in\mathbb{N}\setminus{0}.$ Assume $n$ sensors are initially randomly placed in the hyperoctant $[0,\infty)^d$ according to $d$ identical and independent Poisson processes each with arrival rate $\lambda>0.$ Let $0< s \le v$ be given real numbers. We are allowed to move the sensors, so that every two consecutive sensors are placed at distance greater than or equal to $s$ and less than or equal to $v.$ Fix $a\ge 1.$ Assume that $i-$th sensor is displaced a distance equal to $m(i).$ The cost measure for the displacement of the team of sensors is the sum $\sum_{i=1}^{n}d_i^a$ ($a-$total movement). In this work, we discover and explain a sharp decline and a sharp increase (a threshold phenomena) in the expected minimal $a-$total movement around the interference-connectivity distances $s,v$ equal to $\frac{1}{\lambda}.$